Multigrid Solution of a Lavrentiev-Regularized State-Constrained Parabolic Control Problem

Borzì, Alfio; Andrade, González
February 2012
Numerical Mathematics: Theory, Methods & Applications;Feb2012, Vol. 5 Issue 1, p1
Academic Journal
A mesh-independent, robust, and accurate multigrid scheme to solve a linear state-constrained parabolic optimal control problem is presented. We first consider a Lavrentiev regularization of the state-constrained optimization problem. Then, a multigrid scheme is designed for the numerical solution of the regularized optimality system. Central to this scheme is the construction of an iterative pointwise smoother which can be formulated as a local semismooth Newton iteration. Results of numerical experiments and theoretical twogrid local Fourier analysis estimates demonstrate that the proposed scheme is able to solve parabolic state-constrained optimality systems with textbook multigrid efficiency.


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